To answer this question, let's go through each option to understand why it is correct or incorrect:
Option A) D and C - This option is incorrect because if B is sitting beside F, then C cannot be one of the neighbors of B because A does not like C and doesn't sit beside or opposite C.
Option B) E and C - This option is incorrect for the same reason as Option A. If A is sitting beside F, then C cannot be one of the neighbors of B.
Option C) D and E - This option is correct. If A is sitting beside F, then B must be sitting opposite A. In this case, the two neighbors of B would be D and E.
Option D) None of these - This option is incorrect since we have found the correct answer in Option C.
Therefore, the correct answer is option C. The two neighbors of B are D and E.